In a microcavity, this picture needs to be modified in number
of important ways.[1]}, [2]}, [3]}, [4]}, [5]} First, the correct quantum mechanics basis includes the quantized radiation field states into the atomic or molecular basis. We denote these as \(|\phi ;n_k\rangle \)  where \(\phi \)  denotes the material (atomic, molecular, etc.) state while \(n_k\)  denotes the number of quanta (photons) in the \(k\) -th mode of the radiation field. Thus, a molecule in the ground state with a cavity devoid of photons would be denoted as \(|g;0_k\rangle \)  with energy \(E_g+ \hbar \omega _k\) . This is depicted in Fig.REF  in which to a first approximation the electronic potential surfaces are vertically shifted in energy by \(\hbar \omega _kn_k\) . For clarity, we show the case for a single mode cavity with frequency \(\omega _c\) . If the cavity is resonant or nearly resonant with the optical transition frequency, \(\omega _x\) , the adiabatic potential for the \(|g;n_k\rangle \) 
(i.e. molecular ground state + \(n_k\)  cavity photons) intersects the potential for the \(|e;(n_k-1)\rangle \)  (i.e. molecular excited state + \(n_k-1\)  cavity photons) near the Franck-Condon point. Coupling between the radiation field and the atomic or molecule state,
introduces a new set of eigenstates of the matter/radiation field which are linear combinations of the dressed-atom states termed lower (LP) and upper (UP) polaritons.

(
c
|Lk(nk)
